The law can be regarded as a reflection and love is the source. The reflection can never be greater than the source.
This is evident even in the common law legal system where there is the "spirit of the law." Thus a magistrate will take into account the mitigating circumstances surrounding an offense and rule accordingly.
The letter kills but the spirit brings life. If the law brings righteousness then the letter would kill and David would have sinned when he ate the shewbread.
I think this goes hand-in-hand with the topic of this thread: Are Law and Grace Opposites? In Matthew 12:7-8 Jesus says, "If you had known what these words mean, ‘I desire mercy, not sacrifice,’ you would not have condemned the
innocent. For the Son of Man is Lord of the Sabbath." Here I believe Jesus is saying that they condemned him for transgressing the Sabbath, but he was
innocent of transgressing the Sabbath.
Mark 2:27-28 Then he said to them, "The Sabbath was made for man, not man for the Sabbath. So the Son of Man is Lord even of the Sabbath." Again, I believe this shows that Jesus is Lord of the Sabbath and decides how it should be obeyed. And how it should be obeyed should be for our benefit (the benefit being focused on resting and whatever will help us rest). In Matthew 12:11-12 Jesus even says that it is lawful to do good on the Sabbath. "He said to them, 'If any of you has a sheep and it falls into a pit on the Sabbath, will you not take hold of it and lift it out? How much more valuable is a person than a sheep!
Therefore it is lawful to do good on the Sabbath.'"
So since the priests attend to God on the Sabbath, the priests' transgression he was referring to must not have been the transgression of God's Law but the transgression of Man's Law (Pharisaical Law/what-have-you).
Jesus even says that the priests desecrate the Sabbath but are innocent. How can they be innocent if they are desecrating the Sabbath? There must be two laws at work here. One must be Man's Law and another must be God's.
I believe the letter of the Law is very important, but you are right; we cannot remove its spirit, which is love. As an aside, it is even explicitly stated that during some Sabbaths in the Torah one should do no work, but that they
may prepare food to eat.